Internal problem ID [12695]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+2 y t=4 \,{\mathrm e}^{-t^{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(y(t),t)=-2*t*y(t)+4*exp(-t^2),y(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t^{2}} \left (4 t +3\right ) \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 18
DSolve[{y'[t]==-2*t*y[t]+4*Exp[-t^2],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t^2} (4 t+3) \]